When was the last time you met a new play that was so smart it made your head spin? Not in years, huh? Well, get ready to reel, New York. Anne Washburn’s downright brilliant “Mr. Burns, a Post-Electric Play” has arrived to leave you dizzy with the scope and dazzle of its ideas.

This intoxicating and sobering vision of an American future, set during a day-after-tomorrow apocalypse, isn’t just some giddy head trip, either. It has depths of feeling to match its breadth of imagination. At the end of Steve Cosson’s vertiginous production, which opened on Sunday night at Playwrights Horizons, you’re likely to feel both exhausted and exhilarated from all the layers of time and thought you’ve traveled through.

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Excerpt: 'Mr. Burns'

A scene from Anne Washburn's "Mr. Burns, a Post-Electric Play," at Playwrights Horizons.

You may also feel a burning urge to tell somebody about what you’ve just seen, even though you know you won’t get the details exactly right. This is appropriate to your experience of “Mr. Burns,” which was staged in 2012 at Woolly Mammoth Theater Company in Washington. The vital instinct to pass on and share stories, inevitably reshaping them along the way, is what this show celebrates.

Portraits of our fragile little planet laid siege — whether by aliens, zombies or human warmongers — are a dime a dozen in multiplexes and on television screens, occasions for big explosions that light up the sky. “Mr. Burns,” in contrast, is rather quiet. And since the world it portrays has been robbed of electricity, much of it takes place amid shadows or in candlelight.

But, ah, the colors that can be conjured out of the dark by people struggling to forget how scared they are. On one level, “Mr. Burns” is a latter-day relative of “The Decameron,” Boccaccio’s 14th-century masterwork about young Italians swapping narratives in a deserted villa, where they have fled the Black Death.

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Mr. Burns, a Post-Electric Play, at Playwrights Horizons, imagines a post-apocalyptic world (created by the writer, Anne Washburn) that is comforted by pop-culture references and, especially, a plot from “The Simpsons.”Credit
Sara Krulwich/The New York Times

The first characters we meet in “Mr. Burns” are clearly on the run from something like a plague, too (radioactivity, to be exact, after the mass failure of nuclear power plants across the country). Gathered around a fire in a woods, these random survivors — like the sequestered Florentines of “The Decameron” — are waiting out a nuclear winter by reimagining a great classic tale of their time. That would be an episode of “The Simpsons,” the “Cape Feare” episode, to be exact, in which young Bart — the son of Homer and Marge — is stalked by the murderous Sideshow Bob.

Let’s pause for a second and note that it might be helpful if you have a passing knowledge of “The Simpsons,” Matt Groening’s long-lived animated series that finds gloriously inventive form and function in the dysfunctional all-American family. You need to know at least that “The Simpsons” is the most inspired American cultural compactor of the past 50 years, which is saying something in an era in which most culture is a matter of recycling.

That “Cape Feare” segment that’s being reconstructed from memory at the beginning of “Mr. Burns”? It is partly a riff on the 1991 Martin Scorsese movie, “Cape Fear,” a remake of a 1962 film that starred Robert Mitchum, whose earlier role in “The Night of the Hunter” is also cited in “The Simpsons” episode under discussion, along with some Gilbert & Sullivan operettas.

So you see, what the characters in “Mr. Burns” are trying to recollect in the play’s first act is itself a recollection of many stories, variously told, that came before. And during the 80-some years covered in “Mr. Burns,” that tale made up of other tales will evolve into other shapes until, at the end, we have come full circle. And what we’re returning to is not that original “Simpsons” episode, but something far older and more primal. (I don’t want to give away too much, but in the astonishing final sequence, the composer Michael Friedman has devised a fabulous score that turns Britney Spears and Eminem hits into chthonic chorales.)

This may all sound too clever and ironic, or — to use a prefix turned tiresome adjective — too meta. Yet “Mr. Burns” is also passionately sincere in a way that puts to shame most frivolous postmodern game-playing.

That single “Simpsons” episode becomes a treasure-laden bridge, both to the past and into the future. And in tracing a story’s hold on the imaginations of different generations, the play is likely to make you think back — way back — to narratives that survive today from millenniums ago. Every age, it seems, has its Homers.

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Jennifer R. Morris and Matthew Maher in "Mr. Burns, a Post-Electric Play."Credit
Sara Krulwich/The New York Times

Ms. Washburn’s blasted America, which is made to feel as imminent as next week, has been rendered without distancing archness or air quotes. As designed by Neil Patel (sets), Emily Rebholz (costumes), Justin Townsend (lighting) and Ken Travis (sound), the play’s look is that of our own present, just slightly tweaked by catastrophe. (Bravo, too, to Sam Hill’s masks and wigs and Jeremy Chernick’s sui generis special effects.) We are reminded of how ordinary life can seem in moments of extraordinary crisis, of how horror creates its own quotidian routine.

It’s easy to forget how good the acting is here because it doesn’t feel like acting, except when the characters are putting on a show, and then we’re always aware of the real people beneath the disguises. (Their characters even act in character.) Ms. Washburn has written that she and Mr. Cosson assembled actors in 2008, all members of the Civilians troupe (and most of whom appear in this production), to try to recall “Simpsons” episodes among themselves. Much of the dialogue in the first act comes verbatim from those sessions. And the eight-member cast has retained that spontaneous sense of effortful recollection.

Since context changes the way words sound, even the most banal exchanges feel fraught. We hear the anxiety in the silence that surrounds these survivors of a nuclear holocaust, and the bereftness in their ways of finding order in loss. Hollywood, by the way, could take a lesson from Ms. Washburn, who has managed to be just specific enough to suggest a futurist world with its own rules and without the holes in logic that plague so many blockbusters.

I keep biting my tongue (or my keyboard-hitting fingers) because “Mr. Burns” has so much to say about so many important subjects and arrives at these perceptions so organically. (The title refers to another “Simpsons” character, of particular relevance to a show involving a nuclear disaster.) And I don’t want to give away more than I have already.

But you should know that the second act, set seven years after the first, manages to provide an instant lesson in the processes of capitalism. And that it asks us implicitly to rethink the nature and value of art, which in this case includes television commercials and Top 40 singles.

Who knows what art will finally be remembered, or if the Simpsons will join the pantheon of those mainstream entertainers of another age, Homer and Shakespeare? Yet with grand assurance and artistry, Ms. Washburn makes us appreciate anew the profound value of storytelling in and of itself.

Not incidentally, “Mr. Burns” also makes a case for theater as the most glorious and durable storyteller of all. I look forward to remembering it for a long, long time.